Question

Which is a stretch of an exponential decay function?

Answer 1

Answer:

The correct option is C. The function $f(x)=\frac{5}{4}(\frac{4}{5})^x$ is a stretch of an exponential decay function.

Step-by-step explanation:

The general form of an exponential function is

$f(x)=ab^x$

where, a is the initial value and b is the growth factor.

If b<1, then it represents a decay function and if b>1, then it represents a growth function.

Let k be a stretch and compression factor.

$g(x)=kf(x)$

If k<1, then it represents vertical compression and if k>1, then it represents vertical stretch.

In third function

$f(x)=\frac{5}{4}(\frac{4}{5})^x$

$k > 1$

$b < 1$

Therefore the function $f(x)=\frac{5}{4}(\frac{4}{5})^x$ is a stretch of an exponential decay function.